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interprime n.  and  pronic n.

First numbers that belong to both sets:

6, 12, 30, 42, 56, 72, 240, 342, 420, 462, 506, 552, 600, 650, 870, 1056, 1190, 1482, 1722, 1806, 2550, 2652, 2970, 3540, 4422, 6320, 7140, 8010, 10302, 12656, 13572, 14042, 17292, 18360, 19182, 19460, 20022, 22952, 23562, 24180, 27060, 29070, 29756, 31152, 33306, 35156, 35532, 39006, 41412, 42642, 43890, 46440, 46872, 47306, 47742, 52212, 52670, 53592, 55932, 56882, 60762, 67860, 68906, 75350, 76452, 79806, 83232, 84390, 84972, 87320, 88506, 91506, 92720, 95790, 96410, 98910, 99540, 100806, 104006, 111222, 113906, 120756, 123552, 127092, 133590, 143262, 147840, 151710, 156420, 158006, 160400, 164430, 177662, 181050, 184470, 205662, 207480, 208392, 211140, 215760, 223256, 229920, 232806, 245520, 250500, 268842, 281430, 291060, 304152, 308580, 309692, 314160, 325470, 330050, 336980, 348690, 351056, 385020, 387506, 390000, 397530, 398792, 402590, 415380, 438906, 441560, 446892, 464442, 471282, 472656, 475410, 486506, 506232, 514806, 519120, 530712, 539490, 543906, 552792, 572292, 579882, 589056, 593670, 599850, 613872, 637602, 674862, 679800, 681450, 688070, 713180, 761256, 778806, 792990, 810900, 832656, 838140, 839972, 903450, 909162, 911070, 941870, 949650, 955506, 963342, 973182, 1003002, 1033272, 1053702, 1055756, 1066056, 1068122, 1118306, 1141692, 1171806, 1206702, 1208900, 1224342, 1278030, 1303022, 1309880, 1321350, 1349082, 1358390, 1391220, 1417290, 1424442, 1441200, 1475010, 1489620, 1521522, 1553762, 1576280, 1588860, 1624350, 1637120, 1657656, 1670556, 1678320, 1691300, 1696506, 1712172, 1743720, 1756950, 1780890, 1788906, 1804992, 1842806, 1850960, 1861860, 1864590, 1878270, 1881012, 1905780, 1972620, 2000810, 2006472, 2017820, 2020662, 2106852, 2153556, 2233530, 2275572, 2330202, 2339370, 2342430, 2363906, 2397852, 2453922, 2529690, 2568006, 2577630, 2635752, 2684682, 2694522, 2697806, 2714256, 2734062, 2753940, 2760582, 2881506, 3022382, 3025860, 3043280, 3050262, 3053756, 3071256, 3131130, 3166620, 3195156, 3198732, 3202310, 3252612, 3263442, 3336102, 3394806, 3416952, 3435462, 3442880, 3450306, 3495030, 3498770, 3513750, 3528762, 3532520, 3536280, 3555110, 3558882, 3562656, 3676806, 3746160, 3765540, 3769422, 3777192, 3784970, 3835722, 3851406, 3871056, 3890756, 3906552.

Some larger examples :